Traditional scanning spectral imagers acquire two spatial dimensions of the signal on a focal plane array (FPA), and use successive FPA frames in time and a spectral modulator to acquire the spectral dimension. This approach is only effective for scenes that are temporally static over the duration of the spatial/spectral data acquisition (acquisition of a “hypercube”). For fast changing events, such as transient phenomena, either the modulation rate of the spectral modulator or the frame rate of the FPA, or both, must be increased dramatically. Alternatively, in the “single-shot” approach to spectral imaging, the entire spectral/spatial image is acquired in a single FPA frame. To synthesize three dimensions from a two dimensional focal plane array, at least two dimensions must be multiplexed, that is, combined in such a way that spectral and spatial components can be unambiguously redistributed into their respective dimensions using post processing transformations.